Antennas and lines: keep the reference, length, and pattern separate

Extra antenna questions reward bookkeeping more than memorized hardware names. Before calculating, write down the gain reference. Before transforming an impedance, write down the termination and electrical length. Before judging a direction-finding pattern, count nulls rather than looking for the largest lobe.

A three-pass method

ERP and EIRP use the same link-budget arithmetic but different antenna references. Gain in dBd is relative to a half-wave dipole, so the result is ERP. Gain in dBi is relative to an isotropic radiator, so the result is effective isotropic radiated power. Keep all quantities in decibels until the additions and subtractions are complete; then apply the single power multiplier. Antenna gain concentrates power by direction and does not create additional total power.

Electrical length is longer than the same physical length in free space because a dielectric slows the wave. Velocity factor is wave speed in the line divided by the speed of light, and it is set mainly by the dielectric material. Once the line length is expressed electrically, use the termination map. An exact half-wave reproduces an open or short at its input. An exact quarter-wave inverts one into the other. Between zero and a quarter-wave, a shorted lossless section supplies inductive reactance, while an open section supplies capacitive reactance.

A small wire loop has a figure-eight response with nulls separated by 180 degrees, leaving an ambiguity after one bearing. Combining its output with an omnidirectional sense signal of the proper amplitude and phase changes the response to a cardioid: cancellation occurs on only one side. That single deep null is the useful feature. An electrostatic shield solves a different problem by reducing unbalanced capacitive pickup from the surroundings so the loop's nulls remain deep and symmetrical.

Where the distractors pull you

• Replacing radiated power with an AC-power or response-width term. Power factor, apparent power, and half-power bandwidth do not fold antenna gain and system loss into a directional radiated-power figure.
• Treating a dBi figure as the same numeric gain over a dipole, or adding the reference offset in the wrong direction. A half-wave dipole already stands 2.15 dB above isotropic, so converting dBi to dBd requires subtracting 2.15 dB.
• Blaming electrical length on skin effect or faster propagation in coax. The dielectric slows the wave, so a physical cable represents more phase than the same distance in air.
• Assuming every shorted line looks like a short. A half-wave repeats a short, but a quarter-wave turns it into a very high input impedance; the transform is controlled by electrical length.
• Using a loop shield as a matching, gain, bandwidth, or out-of-band filter device. Its relevant job is removing unbalanced capacitive coupling that would fill or shift the nulls.
• Treating a sense antenna as a sensitivity, elevation-diversity, or multipath-cancellation accessory. It resolves the loop's two-direction ambiguity by changing the combined response to a one-null cardioid.

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